Motivated by recent research of Nikitin et al. [J. Phys. D: Appl. Phys., 2009, 49, 055301], we examine the effects of interatomic interactions on adatom surface diffusion. By using a mean-field approach in the random walk problem, we derive a nonlinear diffusion equation and analyze its solutions. The results of our analysis are in good agreement with direct numerical simulations of the corresponding discrete model. It is shown that by analyzing a time dependence of adatom concentration profiles one can estimate the type and strength of interatomic interactions.